Determination of MW distribution of polymers by the liquid chromatographic methods with concentration or mass selective detectors is a simple, affordable solution for process quality control or research and development of synthetic and natural polymers. Absolute methods with molecular weight and viscosity detectors are more demanding and not always affordable.
Using this methods, precision and accuracy of calculated values is of prime importance. GPC/SEC is presently the most common method for determination of molar masses and molar mass distributions of synthetic polymers. It is known for its high intra-laboratory repeatability (precision) of the molar mass data, often better than +/- 5%. At the same time, GPC suffers from a rather low inter-laboratory reproducibility (accuracy). The molar mass data scatter is +/- 10-20% at best and often may reach even several hundreds of percent. In this note, we will discuss the potential sources of errors during GPC data.
The factors influencing the GPC data, like column quality (resolution, efficiency), sample preparation, sample concentration and volume, extracolumn dispersion, sample/solvent/column interactions, detector sensitivity and linearity, instrument flow rate and temperature stability are outside scope of this note and are widely discussed elsewhere.
Factors influencing data processing in GPC/SEC
The data processing in chromatography software consists of data acquisition, integration, calibration and calculation of the results. The possible problems in those areas will be discussed.
Analog signal is usually acquired from detector using A/D converter. To avoid viscosity effects, the lovest detectable sample concentrations are preferable, thus the signal measured is usually low. The range for dataacquisition should thus be selected to use all the board resolution. On some types of detectors, the scaleable recorder output could give better signal/noise ratio than the integrator output. The peaks are usually wide, thus data acqusition frequency can be set to the minimum.
Peak width and threshold definition are the base parameters for the integration algorithm to locate the peak starts and end. In standard chromatography, the peak width of the narrowest peak of interest is recommended as starting point. For wide polymer peaks, it can lead to some signal deformation and information loss. The peak width of the low molecular markers should be used instead. The peak width parameter also defines, how many points from the original data will be used functioning like a some kind of a filter. As its setings will influence the determined retention times to some extent, it is essentiall to use the same value for integration of narrow standand peaks and wide unknown polymer peaks. The threshold parameter together with the peak with determines where the peak starts and ends will be located. The value equal twice baseline noise is a good starting point.
Major source of errors and ambiquities in GPC evaluation is the determination of the peak start and ends and the baseline setting. Especialy the Mn (number average) values are extremely sensitive to peak end detection and the type of baseline separation (baseline versus valey to valey). Similarly, the M(z+1) and Mz averages are sensitive to the peak start definition. High quality instrumentation and columns are the necessary prerequisite for correct interpretation of tailing peaks the peak tail can be either low molecular polymer or instrument al artefact. The determined Mn values can differ by several hunderts % for the possible interpretations.
Without absolute MW detector the GPC/SEC system must be calibrated with appropriate polymer standards. The elution time is related to molecular size, not to the desired molecular weight. The molecular size is dependent also on polymer structure, solvent and temperature. For calibration, standards of the same polymer should have to be used in ideal case, however this is not always possible. Chromatographic software usually supports several calibration options. The most commonly used is narrow standard calibration.
Well defined polymer standards with narrow MW distribution are commercially available for wide range of polymers. The declared Mp values can be directly used for construction of calibration curve. However, they are not available for all polymers, and with the exeption of the most common ones are usually quite expensive. Most commonly the readily available polystyrenes are used for calibration. Resulting molar mass should be then designated polystyrene equivalent molar mass.
The selection of appropriate curve fit for the calibration data is of prime importance. The prerequisite for precise data is use of high resolution columns and enough points to characterise the column set properties. The unknown polymer should be within the calibration curve range, the extrapolation should be avoided. For so called linear columns the linear regression is appropriate in their working range, the cubic curve may fit better at the extremes. For higher polynomial fits, (4 or more) there must be enough points with high reproducibility. The software should check for curve monotonicity in the valid range and should not allow the use of curve showing local maxima or minima.
Dependence between molecular size and molecular weight can b e described by Mark Houwink equation. The parameters K and Alpha can be found in literature or determined by independent methods. This is used in the universal calibration method. We can calculate molecular mass of unknown polymer by using a calibration for another (more common) polymer. We must know the appropriate K and Alpha constants for both polymers at the measurement conditions. The problem with this method is, that the found values can vary widely and the determination is laborious and also prone to errors.
Broad standard calibration
Another approach uses so called broad standard calibration. The characterized broad MW distribution standards are available for wider range of polymers. Alternatively, typical samples/products can be characterized by classical methods or by GPC/SEC with absolute detectors and used as broad standards. With this method, a calibration curve is constructed to fit the measured peak shape to the declared Mw/Mn values or Mw distribution table. Because the declared or determined Mn values are usually prone to significant errros, the use of single broad standard calibration can lead to a great uncertainity in the results. Software supporting multiple broad standard calibration allows a use of several broad standards and thus eliminates this common problem.
Flow rate correction
The calculations of elution volume are based on flow rate the drop counters and other direct volume measuring devices are no more in common use. The calculated values are extremely dependent on the flow rate 1% change in flow rate can cause 10-20ˇ% change in measured Mw values. The flow rate correction method is commonly supported in the chromatography software. Marker (internal standard) is added to standards and samples. Correction is calculated on the basis of difference in marker RT, it usually scales the time axis. It thus can compensa te for different flowrates (using different pump, leaking pump head seals etc.), however will not compensate for fluctuating flowrate by faulty valves, air bubles (causing in fact some offset of time axis). The same concentration of marker, well resolved from system peak disturbances, must be used or otherwise the marker RT concetration or matrix dependence can cause an additional error instead of the expected improvement.
To produce not only precise but also accurate molecular weight data by GPC/SEC, besides the proper instrumentation and methods, the data processing must not be neglected. In this note, we tried to point out the common sources of problems in use of chromatography software for evaluation of GPC/SEC data.
Fig. 1. Effect of baseline setting
Integration of polymer peak with too high threshold (B01), valey to valey (B02) or baseline peak separation (B03) is compared with respect to resulting differences in MW distribution and averages.
Fig. 2 Effect of calibration curve fit
Even with practically linear calibration column set, significant differences in results especially in extrapolated regions occur by using different regression line polynom degree.
Fig. 3 Effect of flow rate correction
The results without and with flow rate are demonstrated on the same chromatogram scaled +/- 5% original size on time axis.